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\begin{document}

\noindent
{\Large 
Geometry Worksheet II \hfill Name:\underline{\hspace{2.8in}}\\ \\
MA~202 \\
Spring Semester 2004}
\vspace{.25in}

\noindent
{\bf WARNING:}  You must {\bf SHOW ALL OF YOUR WORK}.  You will receive 
NO CREDIT if you do not show your work.

\noindent
{\bf DUE:} {\bf ????} 
\begin{enumerate} 
\item Consider the curve and the points $A$--$E$ shown below.  Which of the
points are inside the curve?  Which of the points are outside the curve?
Justify your answer.
	\begin{center}
	\epsfysize 4in
	\epsffile{pictures/curve3.eps}
	\end{center}
\item 
	\begin{enumerate}
	\item Complete the chart below.
	\begin{center}
	\begin{tabular}{|c|c|c|c|}
	\hline
	& {\bf Number} & {\bf Number} & {\bf Number} \\
	{\bf Solid} & {\bf of} & {\bf of} & {\bf of} \\
	& {\bf Vertices} & {\bf Edges} & {\bf Faces} \\
	\hline
	\hline
	Cube &&& \\
	\hline
	Tetrahedron &&& \\
	\hline
	Octahedron &&& \\
	\hline
	Icosahedron &&& \\
	\hline
	Dodecahedron &&& \\
	\hline
	Triangular Prism &&& \\
	\hline
	Quadrilateral Prism &&& \\
	\hline
	Pentagonal Prism &&& \\
	\hline
	Hexagonal Prism &&& \\
	\hline
	$n$-gonal Prism &&& \\
	\hline
	Triangular Pyramid &&& \\
	\hline
	Quadrilateral Pyramid &&& \\
	\hline
	Pentagonal Pyramid &&& \\
	\hline
	Hexagonal Pyramid &&& \\
	\hline
	$n$-gonal Pyramid &&& \\
	\hline
	Cuboctahedron &&& \\
	\hline
	\hline
	Snub dodecahedron &&& \\
	\hline
	\end{tabular}
	\end{center}
	\item Verify Euler's Formula for each of the solids in the chart.
	\end{enumerate}
\item Do problem numbers 1--2, 6--8, 10--10, 17 and 21 from Section 11.3.
\item 
The town of K\"onigsberg included two islands in the middle of the
Pregel River and land on the bank of each river.  There were seven bridges
connecting the islands and the banks of the river. (See the picture below.)
\begin{center}
\leavevmode
\epsfxsize = 3in
\epsffile{pictures/kbridge.eps}
\end{center}
The town people wanted to know if there was a way to walk across each
bridge exactly once.  The path could start anywhere and need not end where
it started.  
\be
\item Draw a graph that corresponds to this problem.
	\vspace{3in}
\item Is there a way to travel over each bridge exactly once?  You must
justify your answer by citing a theorem and explaining how you arrived at
your answer by using that theorem.
\ee
\item Do problem numbers 5--7 in Section 11.4.
\item Verify Euler's Formula for Connected Planar Networks for each of the
networks in Exercise 1 of Section 11.4.
\item Can Euler's Formula for Connected Planar Networks be applied to the
network shown below? Explain.
\begin{center}
\epsfxsize 2in
\epsffile{k5.eps}
\end{center}
\item Do problem number 22 in Section 11.2.
\item Do problem number 25 in Section 11.2.
\item What is the definition of a circle?  How could you use a push pin, a
piece of string, and a pencil to draw a circle?  
\item What is mean by the center of a circle?  a chord of a circle?  
a diameter of a circle?  a tangent line of a circle?  an
arc of a circle?  a sector of a circle?
\item Draw a circle.  Draw a tangent line to the circle.  Draw the radius
of the circle that touches the tangent line. What can you say about the
radius and the tangent line?  Verify your statement for your drawing.
\end{enumerate}
\end{document}
